I. Baraffe (University of Exeter - CRAL-ENS Lyon)

T. Goffrey, J. Pratt, T. Constantino, M. Viallet R.Walder, D. Folini, M. Popov

Convective Boundary Mixing in stars:A new approach based of multi-dimensional hydrodynamics models

Long standing problem affecting chemical mixing, age of stars, transport of angular momentum and magnetic field, …

The problem of convective boundary mixing (overshooting/penetration) in stars

Standard treatment in 1D codes: extra mixing over an arbitrary width dov = 𝜶 HP (𝜶 free parameter)

Envelope

Core

0.5 0.0 0.5 1.0 1.5 2.0

F555W F814W

10

12

14

16

18

20

22

F81

4W

c = 0.3

c = 0.4

c = 0.5

c = 0.6

• Impact of core overshooting (free parameter 𝚲c) on Color-Magnitude diagrams Rosenfield et al. 2017

• Impact on size of convective core, age, surface abundances, etc…..

• Observational constraints from helioseismology: thermal/sound speed profile at the transitionbetween convective envelope and radiative core in the Sun (e.g Cristensen-Dalsgaard osenfield et al. 2011)

• Constraints on convective core size from asteroseismology ⟹ constraints on overshooting efficiency and length (e..g Silva Aguirre et al. 2013; Deheuvels et al. 2016; Bossini et al. 2017; etc…)

• Constraints on convective core size from eclipsing binaries

“Model dependent” methods based on comparisons between observational diagnostics (frequency ratios, mode period spacing, mass/radius, Teff, L, etc…) and predictions from stellar evolution models using different formalisms/recipes for overshooting.

Not so good for eclipsing binaries…..

Question: how reliable are these constraints?

Suggestion of increasing overshooting length with stellar mass (Claret & Torres 2016, 2017, 2018)Reanalysis of 5 eclipsing binary systems ~ 1.2 M⦿ - 4 M⦿ (Constantino & Baraffe, 2018 submitted) Large range of acceptable solutions for the overshooting parameter fos

No trend with mass

∣Constantino & Baraffe 2018

Claret & Torres

For EB to be really useful, one needs → - Very accurate determination of M, R, Teff and Z - Combination with asteroseismology - Better models because of degeneracy of solutions by varying (𝛂MLT, fos, microscope diffusion) (conclusion also reached by Valle et al. 2016, 2017 by analysing synthetic binary systems)

1D models based on phenomenological approaches—> Convection, rotation, dynamo, mixing, turbulence, etc…

Motivation for better models

Calibration of free parameters from observations

👎 no predictive power 👎 degeneracy of solutions 😞 do we really understand the physics?

⇒ Need for multi-dimensional models to improve the 1D formalisms

• Spherical geometry (2D or 3D)• Fully compressible hydrodynamics + rotation• Realistic stellar physics (opacities and equation of state)• Time implicit solver (no stability limit on the timestep)• Initial models from 1D stellar evolution calculation

interface with Lyon code (Baraffe et al.) and MESA (Constantino et al, in prep)

Development of MUSIC “Multidimensionnal Stellar Implicit Code”(Viallet et al. 2011, 2013, 2016; Geroux et al. 2016; Pratt et al. 2016; Goffrey et al. 2017; Pratt 2017)ERC TOFU

Major motivation is to improve phenomenological approaches used in 1D stellar evolution codes

Velocity magnitude : very high res 2432x2048

Analysis of 2D/3D simulations of a star with a large convectiveenvelope and a radiative core (Pre-main sequence star) (Pratt et al. 2016, 2017)

Goal: Derivation of a diffusion coefficient D(r) characterising the mixing in the transitionregion

Penetration regionConvective boundary mixing

Application to convective boundary mixing in stellar envelopes

Radial velocity snapshot

2D3D

inflow: blue outflow: red

Typical shape of the penetration depths (at a given time): extent of downflows beyond the convective boundary varies with colatitude θ

straight average

Straight average miss the larger penetration events

Description of the statistical complexity of the data: Extreme Value Theory Determine the probability of events that are more extreme than any previously observed (used in Earth science, traffic prediction, unusually large flooding event, finance…)

Distribution of maximal penetration depths, linked to extreme events in the tail of the distribution → contribute to mixing

Derivation of a diffusion coefficient D(r)characterising the mixing driven by penetrative plumes

Extreme penetrating plumes characterise the relevant penetration depth in stars(Pratt et al. A&A, 2017)

DEVT

DEV T = D0

1 exp

exp

(rB r) µ

𝜆, 𝜇 are predicted by simulation

rB

D / exp(2z/fos

HP

)Freytag et al. 1996 Herwig et al. 1997

MLT

Very young Sun Pre-Main Sequence Sun

fully convective

The Sun

Radiative core T ~ 3 106 KLi depletes

Application to the depletion of Li in the Sun’s convective envelope

Problem: Models predict less depletion of Li than observed still an open issue!

Observed solar Li ↓

Evolution of Li in a 1 M⦿ with 1D code and our statistical diffusion coefficient

DEVT over dov =0.35 HP

Instantaneous mixing over dov=0.35 HP

Baraffe et al. 2017

need to limit the extension of the overshooting layer to dov ~ 0.35 HP

observed Li foryounger stars

DEVT

MLT

Problem: Li is depleted too rapidly!

no overshooting

DEVT

Application to the depletion of Li in younger clusters (50Myr - 4 Gyr) for a range of masses 0.85 - 1.5 M⦿

Hyades 600 Myr

↑0.85 M⦿

↑1.5 M⦿

Teff

Baraffe et al. 2017

Age (Myr)

Typical rotational evolution of stars

contraction magnetic braking

disc locking

Bouvier 1998

Inspired by our preliminary results for plume penetration, we suggestthe following scenario:

One major hypothesis (that now needs to be checked by further numerical simulations)

The depth of penetrating plumes depends on rotation: fast rotation prevents vertical penetration of plumes (Brummell 2007; Fabregat et al. 2016)

Below a critical Ω (slow rotators), plumes can penetrate deeply (according tothe probability distribution of Pratt et al. 2017) down to a depth dov ~ 1 HP

Above a critical Ω (fast rotators), the plume penetration depth is limited to a given depth dov ~ 0.1 HP

Assuming a simple model for rotation evolution with initially slow and fast rotators for 0.85 - 1.5 M⦿ (as observed in young clusters, see Gallet & Bouvier 2015)

0.85 M⦿

1 M⦿

1.5 M⦿

(=2π

/Ω)

NGC2362 hPer IC2391 Pleaides Hyades NGC6819 NGC6811

→ Ωcrit = 5 x Ω⦿

contraction

magnetic braking

← Observed solar Li

slow

fast

Results for depletion of Li in a 1 M⦿ star adopting mixing according to our statistical diffusion coefficient and assuming that rotation limits the plume penetration depth

Working hypothesis in the overshooting layer: • Ω < Ωcrit —> depth not limited• Ω > Ωcrit —> depth limited to ~ 0.1 HP

slow

fast

Interesting results: trend of Li depletion as a function of age can be reproduced (IC2391 50 Myr to M67 4 Gyr)

Can reproduce the observed correlation between rotation and Li abundance: fast rotators are less depleted

DPratt over dov =0.35 HP

Baraffe et al. 2017

• More work to confirm our main assumption which can explain within the same scenario Li depletion in young clusters and in the Sun

Main assumption: Depth of penetrating plumes depends on rotation with fast rotation preventing vertical penetration of plumes and existence of a threshold in Ω

- Extension of multi-D simulations to different masses/ages and rotation rates - Longer term: explore MHD effects - Analyse the heat transport in the overshooting region

• Test new convective boundary mixing formalisms against observational constraints: - Li as a function of age and rotation in solar type stars - Speed of sound profile in the transition region of the Sun

• Extend our 2D/3D simulations to convective core overshooting: - Can we apply the same statistical approach i.e presence of extreme penetrating plumes responsible for the mixing?

- Test new transport coefficients (chemical species, heat) against asteroseismology Search for signatures on mode properties that can be diagnosed by asteroseimology

Conclusion Next steps

new ERC COBOM

Main conclusion: time implicit fully compressible hydrodynamic code has formidable potentials to provide improvement to phenomenological approaches used in 1D stellar evolution codes.

- Spherical coordinates natural for stellar interiors

- Realistic input physics

- Solve fully compressible hydrodynamical equations

- Time implicit solver—> large timesteps (CFL ~ 10-1000)

—> Cover a range of Mach numbers: from centre (M << 1) to surface M ~ 1 (no need for truncating the surface as e.g anelastic codes) —> speed up the relaxation phase starting from 1D initial model (large time steps + stability) (key to explore a range of parameters)

Conclusion: Some advantages of the MUSIC approach for stellar physics